Kinetics of free-radical polymerization with chain-length-dependent constants under initiation by laser pulses: Effect of chain length dependence of propagation

Nikitin, Anatolij N.; Evseev, A. V.

doi:10.1002/(sici)1521-3919(19990701)8:4<296::aid-mats296>3.0.co;2-o

Cited by 15 publications

(14 citation statements)

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“…The following power law expression22,23 has been proposed for representation of the chain‐length dependence of the propagation rate coefficient where k p 0 and β are constants. The PLP/SEC method yields average 〈 k p L 〉 values which are related to β as follows:9,23 Via Equation (8),23 β is obtained from $\left\langle {k_p^{L_1 } } \right\rangle$ and $\left\langle {k_p^{L_2 } } \right\rangle$ determined for dark time intervals Δ t 1 and Δ t 2 associated with chain lengths $L_2 = \left\langle {k_p^{L_2 } } \right\rangle [{\rm M}]\Delta t_2$ and $L_1 = \left\langle {k_p^{L1} } \right\rangle [{\rm M}]\Delta t_1$ to be β = 0.07 ± 0.02. This number is close to the corresponding exponent estimated from the 〈 k p L 〉 values reported by Olaj et al for MMA at 25 °C 9…”

Section: Resultsmentioning

confidence: 99%

Free-Radical Propagation Rate Coefficients via n-Pulse Periodic Polymerization

Nikitin¹,

Evseev²,

Buback³

et al. 2002

Macromol. Theory Simul.

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Aspects of applying n‐pulse periodic initiation in pulsed laser polymerization/size‐exclusion chromatography (PLP/SEC) experiments are studied via simulation of molecular weight distributions (MWDs). In n‐pulse periodic PLP/SEC, sequences of n laser pulses at successive time intervals Δt1 up to Δtn are periodically applied. With the dark time intervals being suitably chosen, n‐modal MWDs with n well separated peaks occur. The n‐pulse periodic PLP/SEC method has the potential for providing accurate propagation rate coefficients, kp. Among several measures for kp, the differences in molecular weights at the MWD peak positions yield the best estimate of kp under conditions of medium and high pulse laser‐induced free‐radical concentration. Deducing kp from n dark time intervals (corresponding to n regions of free‐radical chain length) within one experiment at otherwise identical PLP/SEC conditions allows addressing in more detail a potential chain‐length dependence of kp. Simulations are compared with experimental data for 2‐pulse periodic polymerization of methyl methacrylate.

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Section: Resultsmentioning

confidence: 99%

Free-Radical Propagation Rate Coefficients via n-Pulse Periodic Polymerization

Nikitin¹,

Evseev²,

Buback³

et al. 2002

Macromol. Theory Simul.

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“…It is also known that the first few addition steps to a newly formed radical occur at a faster rate than monomer addition to long‐chain radicals 6. In the previous work, k

_{p}^{italicL}

was subdivided into two regions with different power‐law exponents,23 as shown for termination above. However, more recently the following expression has been suggested to provide a physically realistic description for propagation of short chains31,34 where $C_1 = (k_{\rm p}^1 - k_{\rm p} )/k_{\rm p}$ and i 1/2 are parameters that dictate the chain‐length dependence of k

_{p}^{italicL}

, k p is the constant value for propagation of long chains, and L c is the chain length separating the two regions with the different chain‐length dependent laws.…”

Section: Methods Developmentmentioning

confidence: 99%

“…The PLP‐MWD technique has been applied to measure k p for many monomers of industrial significance over a range of temperatures, with good agreement (generally within 15%) achieved between facilities around the world;2,17,18 a modified version of the technique has also been used to evaluate chain transfer constants 19–21. In recent years, it has been proposed that some of the minor discrepancies reported in k p values arise from a chain‐length dependence, with monomer addition to short radicals significantly faster than addition to long‐chain radicals;6,22–31 the possible influence of both chain‐length dependent propagation and termination will be considered further in this work.…”

Section: Introductionmentioning

confidence: 99%

Determination of the Mode of Free Radical Termination from Pulsed Laser Polymerization Experiments

Nikitin

Hutchinson

2007

Macro Theory & Simulations

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The molecular‐weight distribution (MWD), obtained by pulsed laser polymerization (PLP) at the high termination rate limit has been considered for investigating termination kinetics. The proposed methodology takes into account both the composite model for termination and the chain‐length dependencies of propagation for short‐chain and long‐chain radicals. Power‐law expressions are used to represent propagation $[k_{\rm p}^L = k_{\rm p}^0 (L)^{ - \alpha } ]$ and termination $[k_{\rm t}^{L,L} = k_{\rm t}^0 (L)^{ - \beta } ]$ of long‐chain radicals (where k p0 and k t0 represent the maximum “virtual” rate coefficients for monomeric radicals, and α and β capture the chain‐length dependencies for propagation and termination), with the combined value of (β − α) evaluated from the MWD, after correcting for the influence of the kinetics of short‐chain radicals. A novel method is also developed for determining the mode of termination, δ, from MWDs produced by PLP at the high termination rate limit. Simulations for methyl methacrylate (MMA) polymerization at 25 °C confirm that the method can be applied robustly in the presence of complicating factors such as chain transfer to monomer and SEC broadening. The analysis of an experimental MWD obtained for MMA polymerization at 25 °C results in estimates of 0.14 ± 0.03 for (β − α) and 0.75 ± 0.04 for δ.

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“…The effect of the dependence of termination rates on chain length has been addressed numerically in refs. [29,30,31,32,33,34,18] which employed various empirical rules for the form of k(M, N ).…”

Section: Introductionmentioning

confidence: 99%

Pulsed Laser Polymerization at Low Conversions: Broadening and Chain Transfer Effects

O’Shaughnessy

Vavylonis

2003

Macro Theory & Simulations

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Pulsed laser polymerization (PLP) is widely employed to measure propagation rate coefficients k p in free radical polymerization. Various properties of PLP have been established in previous works, mainly using numerical methods. The objective of this paper is to obtain analytical results. We obtain the most general analytical solution for the dead chain molecular weight distribution (MWD) under low conversion conditions which has been hitherto obtained. Simultaneous disproportionation and combination termination processes are treated. The hallmarks of PLP are the dead MWD discontinuities located at integer multiples of n 0 = k p t 0 C M , where t 0 is the laser period and C M is the monomer concentration. We show that chain transfer reduces their amplitude by factors e −ctrLn0 , consistent with numerical results obtained by other workers. Here c tr is the chain transfer coefficient and Ln 0 (L =integer) are the discontinuity locations. Additionally, transfer generates a small amplitude continuous contribution to the MWD. These results generalize earlier analytical results which were obtained for the case of disproportionation only. We also considered 2 classes of broadening: (i) Poisson broadening of growing living chains and (ii) intrinsic broadening by the MWD measuring equipment (typically gel permeation chromatography, GPC). Broadening smoothes the MWD discontinuities. Under typical PLP experimental conditions, the associated inflection points are very close to the discontinuities of the unbroadened MWD. Previous numerical works have indicated that the optimal procedure is to use the inflection point to infer k p . We prove that this is a correct procedure provided the GPC resolution σ is better than n 1/2 0 . Otherwise this underestimates Ln 0 by an amount of order σ 2 /n 0 .

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Kinetics of free-radical polymerization with chain-length-dependent constants under initiation by laser pulses: Effect of chain length dependence of propagation

Cited by 15 publications

References 0 publications

Free-Radical Propagation Rate Coefficients via n-Pulse Periodic Polymerization

Free-Radical Propagation Rate Coefficients via n-Pulse Periodic Polymerization

Determination of the Mode of Free Radical Termination from Pulsed Laser Polymerization Experiments

Pulsed Laser Polymerization at Low Conversions: Broadening and Chain Transfer Effects

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